Name
Abstract | ||
|---|---|---|
We consider the Brézis–Nirenbergproblem: {−Δu=|u|2⋆−2u+λuinΩ,u=0on∂Ω,where Ω is a smooth bounded domain in RN,N≥3,2⋆=2NN−2 is the critical Sobolev exponent and λ>0. Our main result asserts that if N≥4 then there exists a pair of sign-changing solutions of the problem for every λ∈(0,λ1(Ω)), λ1(Ω) being the first eigenvalue of −Δ in Ω with Dirichlet boundary conditions, while if N=3 then a pair of sign-changing solutions exists for λ slightly smaller than λ1(Ω). Our approach uses variational methods together with flow invariance arguments. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.aml.2018.04.020 | Applied Mathematics Letters |
Keywords | Field | DocType |
Critical exponent,Nodal solutions,Variational approach,Gradient flow | Exponent,Invariant (physics),Mathematical analysis,Sobolev space,Pure mathematics,Dirichlet boundary condition,Nirenberg and Matthaei experiment,Eigenvalues and eigenvectors,Mathematics,Bounded function | Journal |
Volume | ISSN | Citations |
84 | 0893-9659 | 0 |
PageRank | References | Authors |
0.34 | 1 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tieshan He | 1 | 7 | 2.66 |
| Chaolong Zhang | 2 | 65 | 15.03 |
| Dongqing Wu | 3 | 31 | 5.50 |
| Kaihao Liang | 4 | 1 | 0.96 |